Opposing ideas, placed together, are the stuff of the creative leap. The moments when contradictory ideas coexist have peculiar power. They teach surprising lessons. Years ago, my wife and I went to the old AstroWorld Park where I rode America’s then-largest wooden roller coaster. As I hurtled through space, I suddenly knew two things with absolute certainty. One was: I was going to die. The other was: I was perfectly safe.

It was a delicious moment. Call it opposition in apposition. Another word for it is cognitive dissonance. My entire perspective altered in that lovely contradiction. It is in such moments — such lurches — that we see what we never would’ve seen otherwise.

Those side-by-side contradictions surround us if we’re alert to them. Do I warp a child's sense of reality when I speak of Santa Claus? I doubt it. The child soon enough realizes that coexisting belief and disbelief in Santa is a way of fathoming the real power of generosity.

Or take Orion — that cluster of stars in which we see the giant hunter of myth. When the Hubble telescope gazed into one star of Orion's sword, it showed us a glorious swirling nebula. We know perfectly well that the stars forming Orion are no simple connect-the-dots picture lying in one plane of the sky. But that ghostly hunter, chasing the Pleiades across eternal night, hints at the immensities of meaning that those stars possess.

Engraving of Orion from Johann Bayer’s Uranometria, 1603

One of two things happens when contradictory facts move into juxtaposition. One fact might simply prove wrong, and that's that. But sometimes the contradiction presents two totally different faces of some deeper truth. Opposing realities each gain in validity as they reach that nexus. And our world shifts under our feet.

Hence our title, Darkness and Light: two obvious opposing states, each of which is meaningless without the other. Take the nature of light: Seventeenth-century scientists Huygens and Newton had built conflicting, but plausible, wave and corpuscular theories of light. Which was correct? The contradiction festered for two centuries. Was one right and the other wrong?

Then Planck explained how the energy of light is spread in little chunks among its wavelengths. By then, the wave theory was ascendant. But he upset that apple cart by providing evidence of a corpuscle called a photon. And the mystery only deepened.

It wasn't until the late 1920s that modern quantum mechanics violated all intuition by telling us that material particles reduce to mere waves of probability. Only when we carried the contradictory descriptions to their full validity, and laid them on top of one another, could we make sense of light.

Science is filled with stories like that. For centuries, competing explanations of heat gained validity. Heat was an invisible fluid flowing from hot bodies to cold ones or was it some sort of stored motion in a material? Only after we had an atomic theory could the principle of energy conservation emerge. When it did, both explanations lingered as shadows of a more complex truth.

Of course, science is simple stuff alongside the contradictions of human relationships. Which of us doesn't see kindness and meanness, generosity and greed, all juxtaposed in the people we know? The world does change in those rare moments when we make sense of opposites. So look for contradiction. Out of it, despair can turn to hope. A tiny glint of Orion's sword can open into a vast array of stars and dust, a thousand light years away from the hard earth upon which you and I spend our days.

This year, let’s focus upon this particular contradiction of darkness and light. Let us see where that one pair of opposites takes us. We have, on the one hand, the obvious fact of harnessing darkness and light in photography, spectroscopy, quantum theory ... But these matters call up metaphorical oppositions as well.

What is more intense than the opposition of danger and desirability that swirls around any new idea. As the light bulb of invention clicks on, it invariably incurs the darkness of unintended consequences and disruption, as well.

Invention is born at the nexus of such contradictions. So, as we play with light and darkness, let us be especially alert to the way contradiction serves as the ultimate mother of invention.